Nondegenerate and Nilpotent Centers for a Cubic System of Differential Equations

• Algaba, Antonio ^[1] ; García, Cristóbal ^[1] ; Giné, Jaume ^[2]
  1. [1] Universidad de Huelva

     Universidad de Huelva

     Huelva, España

     
  2. [2] Universitat de Lleida

     Universitat de Lleida

     Lérida, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 333-345
• Idioma: inglés
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• Resumen

  • We consider the autonomous system of differential equations of the form x˙=P1(x,y)+P2(x,y),y˙=Q1(x,y)+Q3(x,y),where Pi and Qi are homogeneous polynomials of degree i. For such systems we provide the necessary and sufficient conditions to have a center at the origin. In fact this family only has nondegenerate and nilpotent centers.